GPS: Parallel Computing and the Value of Teamwork

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

What are possible Sources of Common and Persistent Student Errors in Algebra and Calculus?

Research shows that college students make numerous algebra and other prerequisite content-related errors in Calculus courses. Most of these errors are common, persistent, and often observed in simple mathematical tasks. This qualitative study is an attempt to identify the potential sources of such errors. Based on our observations of student errors, we wrote a Precalculus and a Calculus test and administered them in twelve sections of four different undergraduate mathematics courses for which either Precalculus, Calculus I or both were a prerequisite. The tests were announced on the first day of the class and administered the following week. All the questions on the test were True or False questions. Based on our experience as college mathematics instructors, we assumed that many students would perceive the True answers as False and the False as True. Therefore, if students’ selected a given answer, mathematical statement, process or solution as True, they were asked to justify why that was not False and vice-versa. They were instructed to provide logical explanations and avoid plugging in numbers to check for correctness. Analysis of data using grounded theory approach resulted in the following three possible external sources of common and persistent student errors: a) Difficulty with symbols and/or lack of attendance to the meaning of those symbols, b) Instructional practices, and c) Lack of knowledge. We will provide examples to illustrate how such errors could have originated from these sources.

GPS: How Does It Grow?

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

Mathematical Reasoning of Vocational High School Students on Mathematical Tasks in the Law of Demand Context

This study aims to describe the mathematical reasoning abilities of vocational high school students in the business and management expertise in solving mathematical tasks in the law of demand context. This research uses the descriptive qualitative method. The participants consisted of six students categorized into three groups: high, medium, and low mathematical abilities. Participants from one of the vocational schools in Ciamis, Indonesia. Mathematical tasks to explore students' mathematical reasoning abilities in the law of demand context. The law of demand is a concept in business economics subjects. The task situation expanded as an alternative to solving more mathematical tasks—data from the results of student answers and interviews. Data analysis refers to the characteristics of mathematical reasoning, which consists of imitative and creative reasoning. The stages of data analysis are reduction, presentation, interpretation, inference, and verification. The results of data analysis show that all students tend to do imitative reasoning on each given task. Students tend to remember the law of demand formulas and perform mathematical procedures that they remember. Students often perform mathematical procedures that are not by the nature of mathematics so that the resulting solution is wrong. The law of demand questions designed to explore creative reasoning abilities has not been able to bring students to the flow of creative mathematical reasoning.

GPS: Diving into Dolphin Data

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

SPECIFICS OF TEACHING THE INVERSE RELATIONS BETWEEN THE ARITHMETIC OPERATIONS ADDITION AND SUBTRACTION DURING THE EDUCATION IN MATHEMATICS IN GRADE 1

One of the fundamental knowledge in mathematics in Primary school is related to the arithmetic operations addition and subtraction. According to the educational programs in mathematics in the Republic of Bulgaria, students start studying these operations in grade 1. The article presents theoretical concepts affecting studying the arithmetic operations addition and subtraction in the education in mathematics at a primary school. The research work identified the specifics of studying the inverse connections between the arithmetic operations addition and subtraction in the education in mathematics for grade 1 are also presented. Some of the significant tasks with importance for discovering the relations between the forward operation addition and the reverse operation subtraction were proposed in the study. A new methodology system of work with tasks where these relations are used was developed and tested. The author studied the knowledge, skills, and competencies of the grade 1 students to solve arithmetic operations addition and subtraction tasks. After the exit diagnostic, it was found out that the students of the class where the new methodology system of work was applied during their education in mathematics have got a higher level of knowledge and skills from competency Cluster Numbers in respect of the arithmetic operations addition and subtraction. The use of mathematical tasks with reverse relations between the arithmetic operations addition and subtraction help the students to develop both the overall mathematical knowledge and the logical thinking of the first-graders.

GPS: Trusting Technology

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

ԷՅԼԵՐԻ ՄԵԹՈԴՈՎ ՈՐՈՇ ՏԵՔՍՏԱՅԻՆ ԽՆԴԻՐՆԵՐԻ ԼՈՒԾՈՒՄԸ ՈՐՊԵՍ ՍՈՎՈՐՈՂՆԵՐԻ ՏԵՍՈՂԱԿԱՆ ՄՏԱԾՈՂՈՒԹՅԱՆ ԶԱՐԳԱՑՄԱՆ ԱՌԱՆՁՆԱՀԱՏՈՒԿ ՄԱԹԵՄԱՏԻԿԱԿԱՆ ՄԻՋՈՑ / SOLUTION OF SOME TEXT PROBLEMS BY EULER'S METHOD AS A UNIQUE MATHEMATICAL TOOL FOR DEVELOPING VISUAL THINKING OF STUDENTS

Հոդվածում դիտարկված է Էյլերի տրամագրերի (դիագրամների) միջոցով մաթեմատիկայի դասընթացից բազմություններին առնչվող որոշ խնդիրների լուծման նոր մեթոդական հնար, որը հնարավորություն է տալիս առավել դյուրացնել և ակնառու դարձնել տեքստային խնդիրների լուծումը՝ զարգացնելով սովորողների տեսողական մտածողությունըֈ:/ The article touches upon a new methodological approach to solving some textual mathematical tasks associated with sets using Euler diagrams, which facilitates the solution of mathematical tasks, developing the visual thinking of students.